Mechanics of knots

The simplest type of knots that we tie everyday is known as the overhand knots. The topology of overhand knots is defined by the unknotting number, n ( number of times the knot must be passed through itself to untie it, see figure above). Shoelaces are commonly tied using the reef knot, which comprises two overhand knots each with n=1. We combine experiments and theory to study the mechanics of overhand knots, and essentially answer the question how much force has to be applied to tighten the knot. Excellent agreement is found between theory and experiments for overhand knots over a wide range of crossing numbers.